# 5.12. Beam Remnants¶

Details for the handling of the beam remnants in Sherpa will be described in our forthcoming publication.

Broadly speaking, the beam remnants include the parameterisation of the form factors for hadrons or the hadronic components of photons and the treatment of the beam break-up, most importantly the intrinsic transverse momentum distribution of the partons and how the recoils are distributed.

The following parameters are used to steer the beam remnant handling:

## 5.12.1. BEAM_REMNANTS¶

Specifies whether beam remnants are taken into account, with possible values ‘On’ and ‘Off’.

## 5.12.2. REMNANTS¶

Sherpa organises the remnant handling by particle, with the PDG code as tag-line.

```
REMNANTS:
2212:
KT_Form: Gauss_limited
```

The usual rules for yaml structure apply, c.f. Input structure. Longitudinal momenta for sea partons in hadrons are distributed according to a probability distribution in their light-cone momentum \(x\) given by \(P(x)=x^{-1.5}\). If there are two valence partons left in the beam remnant after the shower initiators have been treated, the first of the two (usually the quark) will have a longitudinal momentum with \(P(x)=\exp(-1/x)\), while the last remaining valence parton (usually the di-quark for nucleons) carries the remaining longitudinal momentum.

For the intrinsic transverse momentum, Sherpa differentiates between the
transverse momentum for shower initiators (`SHOWER_INITIATOR_MEAN`

etc.)
and for beam spectators (`BEAM_SPECTATOR_MEAN`

etc.), and it offers
different strategies to compensate the transverse momentum between the
two sets of partons per beam, see below (`KT_RECOIL`

).

`KT_FORM (default: Gauss_Limited)`

This parameter specifies the scheme to calculate the intrinsic transverse momentum of partons within beams. Available options are:

`Gauss`

: a simple Gaussian with mean and width;`Dipole`

: a dipole form parameterised by \(Q^2\);`Gauss_Limited`

,`dipole_Limited`

: as above but further modified by a polynomial function of the form \(1-(k_{T}/k_{T,\rm{max}})^\eta\), where \(k_{T,\rm{max}}\) and \(\eta\) are given by the`KTMAX`

and`KTEXPO`

tags;`None`

: no intrinsic transverse momentum is assigned.

`KT_RECOIL (default: Beam_vs_Shower)`

Transverse momenta for all partons inside the beam are generated independently from each other according to the form and parameterisation specified for them in

`KT_FORM`

and`SHOWER_INITIATOR_MEAN`

etc., or`BEAM_SPECTATOR_MEAN`

etc.. This will lead to a net residual transverse momentum of partons that needs to be compensated within the beams, to guarantee that the remnants do not create a total beam transverse momentum. Sherpa has implemented two strategies to achieve this:`Democratic`

: the overall residual transverse momentum is distributed over all partons in the beam according to their energies.`Beam_vs_Shower`

: the residual transverse momentum of all spectators is distributed over the shower initiators according to their energies and vice versa.

`SHOWER_INITIATOR_MEAN (default for nucleons: 1.0)`

This parameter specifies the mean in GeV for the intrinsic transverse momentum in case of a limited or unlimited Gaussian distribution.

`BEAM_SPECTATOR_MEAN (default for nucleons: 0.0)`

Same as for

`SHOWER_INITIATOR_MEAN`

.`SHOWER_INITIATOR_SIGMA (default for nucleons: 1.1)`

This parameter specifies the sigma in GeV for the intrinsic transverse momentum in case of a limited or unlimited Gaussian distribution.

`BEAM_SPECTATOR_SIGMA (default for nucleons: 0.25)`

Same as for

`SHOWER_INITIATOR_SIGMA`

.`SHOWER_INITIATOR_Q2 (default for nucleons: 1.1)`

This parameter specifies the \(Q^2\) in \({\rm GeV}^2\) of the limited or unlimited dipole distribution for the intrinsic transverse momentum.

`BEAM_SPECTATOR_Q2 (default for nucleons: 0.25)`

Same as for

`SHOWER_INITIATOR_Q2`

.`SHOWER_INITIATOR_KTMAX (default for nucleons: 2.7)`

This parameter specifies the \(k_{T,\rm{max}}\) in \({\rm GeV}\) of the limited dipole or Gaussian distributions for the intrinsic transverse momentum.

`BEAM_SPECTATOR_KTMAX (default for nucleons: 1.0)`

Same as for

`SHOWER_INITIATOR_KTMAX`

.`SHOWER_INITIATOR_KTEXPO (default for nucleons: 5.12)`

This parameter specifies the \(\eta\) in the equation above that limits the intrinsic transverse momentum distribution.

`BEAM_SPECTATOR_KTEXPO (default for nucleons: 5.0)`

Same as for

`SHOWER_INITIATOR_KTEXPO`

.`REFERENCE_ENERGY (default: 7000)`

This parameter specifies the reference scale in GeV in the energy extrapolation of the mean and width of the Gaussian distribution and of the \(Q^2\) of the dipole distribution of intrinsic transverse momentum, and of the maximally allowed \(k_T\) in the case of limited distributions.

`ENERGY_SCALING_EXPO (default: 0.08)`

This parameter specifies the energy extrapolation exponent.

`MATTER_FORM (default: Single_Gaussian)`

`Double_Gaussian`

can be used to model the overlap between the colliding particles.`None`

switches this off.`MATTER_RADIUS1 (default for nucleons: 0.86, for mesons/photons: 0.75)`

The radius of the (inner) Gaussian in fm. If used with the double-Gaussian matter form, this value must be smaller than

`MATTER_RADIUS2`

.`MATTER_FRACTION1`

Only to be used for double-Gaussian matter form, where it will control the distribution of matter over the two Gaussians. It assumes that a fraction \(f^2\) is distributed by the inner Gaussian \(r_1\), another fraction \((1-f)^2\) is distributed by the outer Gaussian \(r_2\), and the remaining fraction \(2f(1-f)\) is distributed by the combined radius \(r_\text{tot} = \sqrt{\frac{r_1^2+r_2^2}{2}}\). Defaults to

`0.5`

.`MATTER_RADIUS2`

Defaults to

`1.0`

. It is only used for the case of a double-Gaussian overlap, see below.

If the option `BEAM_REMNANTS: false`

is specified at top level, pure
parton-level events are simulated, i.e. no beam remnants are
generated. Accordingly, partons entering the hard scattering process
do not acquire primordial transverse momentum.